Chapter 5: Chromaticism
- Page ID
- 232616
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 5.1: Modal Mixture
- This page discusses modal mixture in music, a technique that borrows notes from parallel keys to alter chord quality while maintaining function, enhancing melodies and harmonies. It's commonly seen in major keys borrowing from minor, with notable examples like tonic and dominant chords and the picardy third. The page includes specific musical examples and assignments to practice understanding and applying this technique.
- 5.2: Neapolitan 6th (♭II6)
- This page discusses the Neapolitan sixth (♭II6), a chromatic predominant chord primarily in first inversion that resolves to ti. It often appears in progressions like ♭II6–V and ♭II6–viio7/V–V, enhancing cadences and sometimes serving as a temporary tonic. The page includes lessons on spelling the chord, analyzing voice leading, and applying it in excerpts, featuring examples from composers such as Chopin and Schubert.
- 5.3: Augmented Sixth Chords
- This page discusses augmented sixth chords, which feature an augmented sixth interval between le and fi. It covers Italian, French, and German variations, their lack of a root, and their resolution to dominant chords. The content includes standard voice leading, cadential uses, and connections to the lament-bass progression. Students are prompted to identify and construct these chords through assignments involving analysis, voice-leading, and music excerpts from composers like Chopin and Joplin.
- 5.4: Common-Tone Chords (CTº7 and CT+6)
- This page explores common-tone diminished seventh (CTo7) and augmented sixth (CT+6) chords, highlighting their roles as embellishments for major triads or dominant sevenths (I or V). Both share a common tone with their respective chords, involved in four-voice textures. CTo7 is derived from neighbor tones, while CT+6 uses chromatic tones. It also examines the relationship between Ger+6 and cad.
- 5.5: Harmonic Elision
- This page discusses harmonic elision, which is the unexpected substitution of chords in a progression. It features leading-tone elision and raised-root elision, altering expected resolutions in harmony. The analysis of harmonic elisions can be performed using Roman numeral analysis to uncover inconsistencies in chords. Examples from Richard Strauss's "Zueignung" illustrate these concepts.
- 5.6: Chromatic Modulation
- This page explores tonal modulation techniques, highlighting methods like pivot chords, common-tone modulation, and enharmonic reinterpretation to facilitate smooth key transitions. It cites composers such as Brahms and Schubert as examples. Additionally, the page addresses the "changing inversion" concept in relation to pivot chords and previews upcoming assignments on diminished-seventh chord respellings, along with links to interactive content.
- 5.7: Reinterpreting Diminished Seventh Chords
- This page explains the role of diminished-seventh chords in chromatic modulation, noting their ability to be enharmonically respelled to connect to distant keys. It mentions that each chord's four notes can serve as the root, leading to resolutions to four different target chords. Additional information regarding project assignments will be provided later.
- 5.8: Augmented Options
- This page discusses the augmented triad, a unique and rare chord in tonal music known for its symmetrical structure and ambiguous nature. It often appears in harmonic minor as III+ or as a chromatic link between V and I. Despite being less common than other triads, it holds significant value and can serve a dominant function.
- 5.9: Equal Divisions of the Octave
- This page discusses how 19th-century composers explored musical ambiguity by avoiding clear tonal centers with equal octave divisions in chord progressions. This departure from traditional diatonic systems destabilized harmonic expectations and introduced new compositional techniques. It identifies five methods of equal octave division: minor second, major second, minor third, major third, and tritone, indicating a shift towards complex pitch organization that influenced 20th-century music.
- 5.10: Chromatic Sequences
- This page discusses diatonic and chromatic sequences in music. Diatonic sequences involve repeating segments in one key, while chromatic sequences alter chords while keeping intervals consistent. Effective voice leading is crucial for both. Diatonic sequences can use secondary dominants and may not follow strict intervals, whereas chromatic sequences can introduce tonal ambiguity.
- 5.11: Parallel Chromatic Sequences
- This page discusses topics on parallel chords, including Parallel 6/3 chords, Parallel Dominant chords, and Parallel Augmented triads, and notes that assignments related to these topics will be available soon.
- 5.12: The Omnibus Progression
- This page describes the omnibus progression, a chromatic sequence with contrary motion between the bass and another voice, used for prolonging dominant harmony or modulating to distant keys. It features smooth voice leading with two variations: converging and diverging. The progression facilitates transitions to similar or first inversion dominant-seventh chords, enhancing access to distant keys.
- 5.13: Altered and Extended Chords
- This page examines altered and extended chords in music, particularly focusing on dominant chords with augmented or diminished fifths and their resolutions. It differentiates between "fake" and "real" chord extensions, illustrating these concepts with examples from composers like Schumann and Schubert. The rarity of 11ths in Western classical music is discussed, alongside their use in various harmonic contexts.
- 5.14: Neo-Riemannian Triadic Progressions
- This page delves into Neo-Riemannian theory, established by Hugo Riemann, which focuses on triadic progressions using transformations like Relative, Parallel, and Leading-Tone Exchange that emphasize common tones. It discusses PLR cycles and related transformations, the categorization of augmented triads, and strategies for modulating between cycles using the "cube dance" model.
- 5.15: Mediants
- This page explores mediant relationships in music theory, classifying them into three types: Diatonic (two common tones), Chromatic (one common tone), and Doubly-chromatic (no common tones). It notes the potential confusion between English and German terms related to these relationships and encourages the use of examples and harmonic analysis for better comprehension.